Kullback Leibler Divergence Based Curve Matching Method

In this paper, we propose a variational model for curve matching based on Kullback-Leibler (KL) divergence. This framework accomplishes the difficult task of finding correspondences for a group of curves simultaneously in a symmetric and transitive fashion. Moreover the distance in the energy functional has the metric property. We also introduce a location weighted model to handle noise, distortion and occlusion. Numerical results indicate the effective of this framework. The existence of this model is also provided.

[1]  Nikos Paragios,et al.  Handbook of Mathematical Models in Computer Vision , 2005 .

[2]  Philip N. Klein,et al.  On Aligning Curves , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Anuj Srivastava,et al.  Analysis of planar shapes using geodesic paths on shape spaces , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Dominik Endres,et al.  A new metric for probability distributions , 2003, IEEE Transactions on Information Theory.

[6]  Laurent Younes,et al.  Computable Elastic Distances Between Shapes , 1998, SIAM J. Appl. Math..

[7]  Daniel Cremers,et al.  Shape Matching by Variational Computation of Geodesics on a Manifold , 2006, DAGM-Symposium.

[8]  Peter N. Yianilos,et al.  Data structures and algorithms for nearest neighbor search in general metric spaces , 1993, SODA '93.

[9]  Hemant D. Tagare,et al.  Shape-based nonrigid correspondence with application to heart motion analysis , 1999, IEEE Transactions on Medical Imaging.

[10]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[11]  Inderjit S. Dhillon,et al.  Clustering with Bregman Divergences , 2005, J. Mach. Learn. Res..

[12]  G. Sandini,et al.  Computer Vision — ECCV'92 , 1992, Lecture Notes in Computer Science.

[13]  Charles C. Tappert,et al.  Cursive Script Recognition by Elastic Matching , 1982, IBM J. Res. Dev..

[14]  Manfred K. Warmuth,et al.  Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions , 1999, Machine Learning.

[15]  L. Bregman.  The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[16]  Nicholas Ayache,et al.  Tracking Points on Deformable Objects Using Curvature Information , 1992, ECCV.